摘要
令H为无限维复可分的Hilbert空间,H上有界线性算子的全体为B(H).用σ(T),σ_(ab)(T)和σ_(a)(T)分别表示为算子T∈B(H)的谱集,Browder本质逼近点谱和逼近点谱.称算子T∈B(H)满足(R)性质,若σ_(a)(T)\σ_(ab)(T)=π_(00)(T),其中π_(00)(T)={λ∈isoσ(T)∶0<n(T-λI)<∞}.主要借助新的谱集给出了算子满足(R)性质新的判定,并进一步得出了算子函数满足(R)性质的充分必要条件.
Let H be an infinite dimensional separable complex Hilbert space and the totality of bounded operators on H is B(H).σ(T),σ_(ab)(T)andσ_(a)(T)denote the spectrum,the Browder essential approximate spectrum and approximate point spectrum of T∈B(H)respectively.T∈B(H)satisfies the property(R)ifσ_(a)(T)\σ_(ab)(T)=π_(00)(T),whereπ_(00)(T)={λ∈isoσ(T)∶0<n(T-λI)<∞}.In this paper,we give a new judgment for operators for which property(R)holds by means of the new spectral set.In addition,the necessary and sufficient conditions for operator functions to satisfy(R)property are explored.
作者
胡添翼
窦艳妮
Hu Tianyi;Dou Yanni(College of Mathematics and Statistics,Shaanxi Normal University,Xi'an 710119,China)
出处
《河南师范大学学报（自然科学版）》
CAS
北大核心
2023年第2期63-69,共7页
Journal of Henan Normal University(Natural Science Edition)
基金
陕西省自然科学基金(2021JM-189).
关键词
(R)性质
算子函数
谱
property(R)
function of operator
spectrum
